On a TV game show, a contestant makes $800 for every correct answer but loses $500 for every wrong answer. After answering 26 questions, Sarah broke even. How many questions did she answer correctly?

If she answered x correctly, then

800x - 500(26-x) = 0
x = 10

Well, it sounds like Sarah was quite the risk-taker on that game show! Let's do some calculation clown-ing.

For every correct answer, she earns $800, and for every wrong answer, she loses $500. Since she broke even, it means that the total money she earned from correct answers was the same as the total money she lost from wrong answers.

Now, let's assume Sarah answered X questions correctly. That means she must have answered (26 - X) questions incorrectly.

On the correct answers, she earns 800X dollars, and on the incorrect answers, she loses 500 times (26 - X) dollars.

Since she broke even, we can set up an equation:
800X = 500(26 - X)

Now let's solve it with some clown math magic.

800X = 500(26 - X)
800X = 500 * 26 - 500X
800X = 13000 - 500X
800X + 500X = 13000
1300X = 13000
X = 13000/1300
X = 10

Voila! Sarah answered 10 questions correctly. Let's applaud her for being a bold contestant!

Let's assume that Sarah answered "x" questions correctly.

For every correct answer, Sarah made $800. So, the total amount she made from correct answers would be 800x.
For every wrong answer, Sarah lost $500. So, the total amount she lost from wrong answers would be 500(26 - x) or 13000 - 500x.

Since Sarah broke even, the total amount she made from correct answers should equal the total amount she lost from wrong answers.

800x = 13000 - 500x

Combining like terms:

800x + 500x = 13000

Simplifying the equation:

1300x = 13000

Dividing both sides by 1300:

x = 10

Therefore, Sarah answered 10 questions correctly.

To solve this problem, let's assume that Sarah answered x questions correctly and (26 - x) questions incorrectly.

For each correct answer, Sarah earns $800, so the total amount earned from correct answers would be 800 * x.

Similarly, for each incorrect answer, Sarah loses $500, so the total amount lost from incorrect answers would be 500 * (26 - x).

Given that Sarah broke even, we can set up the equation:

800 * x = 500 * (26 - x)

We can now solve this equation to find the value of x.

800 * x = 500 * 26 - 500 * x
800 * x + 500 * x = 500 * 26
(800 + 500) * x = 500 * 26
1300 * x = 500 * 26
x = (500 * 26) / 1300
x = 10

Therefore, Sarah answered 10 questions correctly.